Blender Game Engine Python Flipper Animation
The flipper mode belongs to the action armature. This makes the actuator play the animation forward on activation and backward on deactivation.

The actuator uses the internal animation system to play the action in response the the current status (activated or deactivated) and the animation status (playing, reaching end).

The internal animation system can only act according to the animation status. 

The simplest solution is to activate/deactivate the action actuator in flipper mode.

E.g.:

import bge
import math

controller = bge.logic.getCurrentController()
owner = controller.owner

keyboard = bge.logic.keyboard

xyz = owner.localOrientation.to_euler()
xyz[2] = math.radians(180)

if bge.logic.KX_INPUT_ACTIVE == keyboard.events[bge.events.RIGHTARROWKEY]:
    owner.applyMovement((0, 0.08, 0), True)
    owner.worldOrientation = (0, 0, 0)
    controller.activate("turn right")
    controller.deactivate("turn left")
    controller.deactivate("jump")

if bge.logic.KX_INPUT_ACTIVE == keyboard.events[bge.events.LEFTARROWKEY]:
    owner.applyMovement((0, 0.08, 0), True)
    owner.localOrientation = xyz.to_matrix()
    controller.activate("turn left")
    controller.deactivate("turn right")
    controller.deactivate("jump")

if bge.logic.KX_INPUT_ACTIVE == keyboard.events[bge.events.SPACEKEY]:
    owner.applyMovement = ((0, 0, 0.08), True)
    controller.activate("jump")
    controller.deactivate("turn right")
    controller.deactivate("turn left")